Seriesnumber 

 of the Class 

 of Symmetry: 



Elements of Symmetry 



in the 

 considered Crystals: 



I. Tetragonal Systei 



Symmetry of the 



Runtgenpaltern 



)r a plate parallel Ic 



Tetragonal -bisphenoida I j A4 (also = AJ 

 'Tetragonal -pyramidal I A4 

 Tetragonalscalenohe- : A^ {also =: Aj} 



drical 



' Tetragonal -bi pyramidal 

 DitetrHgonal-pyramidal 



Ditetragonal-bipyra 



2Sv- 



A4; HS; 

 A, ; 2 Sv' 



•Trigonal-pyramidal 

 j Trigonal-rhombohe- 

 '■•Tngonal-trapezohe- 

 Trigonal-bipyramidal 

 Ditrigonal-pyramidal 

 Ditrigonal-scalenohe- 



Symmetr^' of the 



Röntgenpattern 



>r a plate parallel t 



1100|: 



Symmetry of '^^ 



Ranlgenpatlern , . Kepresetilalive 



for a plale parallel to Cryslalspecies: 



tllOj: I 



A single quaternary axis I A single horizontal plane 



! of symmetry " 

 A single quaternary axis I A single horizontal plane 



j of symmetry 

 A quaternary axis ; 2 X 2 Two perpendic. planes of 

 planes of symmetry | symmetry ; the perpen- 

 dic. to the photograph. 

 I plate is a binary axis 

 A quaternary axis ; 2 X 2 ; Two perpendic. planes of 

 planes of symmetry ; symmetry ; the perpen- 

 I die. to the photograph, 

 plate is a binary axis 

 A single quaternary axis A single horizontal plate 



j of symmetry 

 A quaternary axis;2X2 Two perpendic. planes of 

 planes of symmetry j symmetry; thepcrpen- 

 I die. to the photograph. 

 I plate is a binary axis 

 A quaternary axis; 2X21 Two perpendic. planes of 

 planes of symmetry | symmetry ; the perpen- 

 dic. to the photograph. 

 I plate is a binary axis 



ot symmetry 



A single horizontal plane 

 of symmetry 



Two perpendic. planes of 

 symmetry; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 



Two perpendic. planes of 

 symmetry; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 



A single horizontal plane 

 of symmetry 



Two perpendic. planes of 

 symmetry; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 



Two perpendic. planes of 

 symmetry; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 



Rutile; Cassiterile; 

 Potass iumferro- 

 cyanide (mimetic) 



Elements of Symmetry 

 I in the 



considered Crystals 



A3. 



A3 (also = Ae) , C 



A3; 3Ai 



Aa; HS 



As; 3Sv 



A3 (aIso = Afl); 3A:;i 



As; s'Aj) HS; 3Sv 



Symmetry of the Symmetry of the 



Röntgenpattern Röntgenpattern j^gp, 



■ a plate parallel to I for a plate parallel to I Crystalspt 



jioTo|: i }T2TÓ!: I 



No symmetry at all No symmetry at all 1 Sodiumper 



(3H.0) " 



No symmetry at all No symmetry at all Phenakite; 



A single vertical pla 



of symmetry 

 A single horizontal pli 



of symmetry 

 A single vertical pla 



of symmetry 

 A single vertical pla 



of symmetry 

 Two perpendic. ph 



symmetry ; the perpen- 

 dic, to the photograph, j 

 plate is B binary axis 



The perpendic. to the platej Quara ; Cinnabar \ 



is a single binary axis 1 

 A single horizontal plane |No mineral known I 

 of symmetry 1 | 



The perpendic. to the plate! Turmaline 



is a single binary axis 

 The perpendic. to the plate CalcHe 

 is a single binary axis 

 . of I Two perpendic. planes of |No n 



symmetry; the perpen- 

 dic. to the photograph. ' 

 plate is a binary axis j 



III. Hexagonal Sys 



'Hexagonal-pyramidal 



Hexagonal- 1 

 Dihexagona 



ipyramidal , Ag; HS; C 



Dihexagonal-bipyram 



3 A.; SAj'; HS; 



i senary axis i A single horizontal plane 



I of symmetry 



y axis and 2 X 3 | Two perpendic. planes of 



i of symmetry symmetrj' ; the perpen- 



I die. to the photograph, 



plate is a binary axis 



A single horizontal plane 



of symmetry 

 Two perpendic. planes of 

 symmetry ; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 

 Two perpendic. planes of 

 symmetry; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 



A single horizontal plane 

 of symmetry 



Two perpendic. planes of 

 symmetry; the perpen- 

 dic. to the photograph, 

 plate is a binary axis 



A single horizontal plane 

 of symmetry 



Two perpendic, planes of 

 symmetry ; the perpen- 

 dic. to the photograph, 

 plate is a binary azis 



Two perpendic. planes of 

 symmetry; the perpen- 

 dic to the photograph, 

 plate is a binary axis 



Apatite 

 Zincite . Wu. 



It may be generally remarked here, that planes of symmetry perpendicular to the photographic plate, will be manifested in the Röntgenpattern by their 

 resp. intersections with the plane ot the photographic plate; and that in the case, where the perpendicular to the plate corresponds to the direction of a binary 

 axis, this will appear in the pallern, as if a symmetry-centre in the photo were present. Binary axes in a plane parallel to that of the photographic plate are 

 of course not revealed in the diffraction-pattern. 



N.B. The symmetry-elements of the Crystals are indicated as follows : An = symmetry-axis of the first order, with a period of ; An = symmetry-axis of the 

 second order (axis of composed symmetry) of the period -; HS^a horizontal plane of symmetry; 5v = vertical plane of symmetry; unequivalcnt axes 



and planes are discerned by accents; f ' = centre of symmetry. The optical axis is always supposed to be vertical: the cristallographical principal axis of 

 the same direction is discerned as the r-axis. In the case of the trigonal crystals, the symbols of Bravais are used ; in the case of hexagonal and trigonal 

 crystals both, the direction of the face (1010) is supposed to be parallel to that of (100) in the tetragonal crystals, and just so that of (l2T0) parallel to 

 that of (010) in the case of tetragonal forms. In some trigonal crystals, the plates were cut parallel to (OlTO) and (fl 10), what does not involve any 

 appreciable difference for the considered problem, but makes it necessary to compaie more directly the corresponding patterns with those obtained from 

 tetragonal crystals cut parallel to (110) and 1 iTo). The symmetry-classes indicated by • are those, whose crystals can appear in enantiomorphous forms. 

 (Enantiomorphism). 



